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-   -   Exact solution of N-S eq. in Kim and Moin's paper (https://www.cfd-online.com/Forums/main/96391-exact-solution-n-s-eq-kim-moins-paper.html)

 Kyounghwa January 21, 2012 07:45

Exact solution of N-S eq. in Kim and Moin's paper

Hello. I'm Kyounghwa.
I'm going on check my New solver for N-S eq.
I have a question.

There are exact solution of N-S eq. about decaying vortices.

u(x,y,t)=-cosx*siny*exp(-2t)
v(x,y,t)=sinx*cosy*exp(-2t)
p(x,y,t)=-1/4*(cos2x+cos2y)*exp(-4t)

These equations are in Kim and Moin's paper.
"Application of a Fractional-Step Method to Incompressible navier-Stokes Equations" in 1985.
This eq. satisfies divergence free.
But, I can't solve by just substituting into Incompressible N-S eq. because the boundary condition of exact solution changes for time(t).

What will I do?
Please, give me an idea. I don't know anything.

I have one more question.

How to obtain a exact solution with boundary conditions of u and v are zero?

 truffaldino January 21, 2012 08:08

Quote:
 Originally Posted by Kyounghwa (Post 340415) Hello. I'm Kyounghwa. I'm going on check my New solver for N-S eq. I have a question. There are exact solution of N-S eq. about decaying vortices. u(x,y,t)=-cosx*siny*exp(-2t) v(x,y,t)=sinx*cosy*exp(-2t) p(x,y,t)=-1/4*(cos2x+cos2y)*exp(-4t) These equations are in Kim and Moin's paper. "Application of a Fractional-Step Method to Incompressible navier-Stokes Equations" in 1985. This eq. satisfies divergence free. But, I can't solve by just substituting into Incompressible N-S eq. because the boundary condition of exact solution changes for time(t). What will I do? Please, give me an idea. I don't know anything. I have one more question. How to obtain a exact solution with boundary conditions of u and v are zero?
This solution is periodic in x and y, just put periodic boundary conditions

 Kyounghwa January 21, 2012 08:57

I don't understand.

Quote:
 Originally Posted by truffaldino (Post 340417) This solution is periodic in x and y, just put periodic boundary conditions

I don't understand.

There is exp(-2t) in equation.
So, u and v change in time. Am I wrong?

 Kyounghwa January 21, 2012 10:05

Quote:
 Originally Posted by truffaldino (Post 340417) This solution is periodic in x and y, just put periodic boundary conditions
You mean...time is fixed?
Then, will I check for one clock?

 cfdnewbie January 21, 2012 11:54

Quote:
 Originally Posted by Kyounghwa (Post 340426) You mean...time is fixed? Then, will I check for one clock?

no, time is notr fixed. What he meant is that the solution stays periodic in space, and decays in time. Just put periodic bcs on your spatial domain!

 Kyounghwa January 23, 2012 10:36

OK~

Quote:
 Originally Posted by cfdnewbie (Post 340434) no, time is notr fixed. What he meant is that the solution stays periodic in space, and decays in time. Just put periodic bcs on your spatial domain!

Ok. I'm understanding.
I will try to do. And I will report.
Thanks.

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